Discarding old laptops
In our area, we have an organization that accepts old computers and parts. They support and employ people with disabilities by using these parts to build computers for them. They have programs to help disabled folks find jobs, get food and housing, etc. If they receive parts that are just too old to use, they disassemble and recycle the recyclable parts. We donate computer-related stuff to them for this purpose.
Perhaps you have an organization like that in your area?
Usually about twice each year there is a special 'dump week' for old electronic/electrical items. This is coordinated with a local entity, in our county it is the Extension Service. I believe they sort through them before demolition of some sort to recover useable parts worth the effort to save. Everything from laptops and printers to toasters and microwave ovens.
My friend Hunter just drops them off at a repair center.
Drilling holes through a hard drive is the standard manner of rendering them finally inoperable. You don't need to be dainty, just drill through the laptop and all. As for recycling old computers, there are several recyclers in my area that will take them for free. You probably have a few in your area, also.